A192454 Number of primes in the range [2^n-n, 2^n+n].
0, 2, 3, 3, 3, 3, 3, 2, 3, 3, 4, 2, 3, 2, 1, 3, 5, 3, 6, 2, 5, 4, 3, 5, 2, 0, 2, 0, 2, 2, 5, 3, 3, 4, 1, 1, 4, 4, 2, 4, 2, 3, 4, 2, 4, 0, 2, 3, 1, 0, 2, 1, 3, 2, 2, 4, 3, 5, 2, 1, 1, 6, 1, 2, 4, 1, 3, 7, 4, 2, 3, 2, 1, 2, 5, 3, 4, 6, 3, 3, 2, 4, 5, 2, 5, 2, 7, 3, 1, 7, 4, 3, 2, 3, 2, 4, 5, 0, 5, 0, 2
Offset: 0
Keywords
Examples
a(1) = 2 because two primes in the range [1^2-1, 1^2+1], a(2) = 3 because 2, 3 and 5 are in range [2^2-2, 2^2+2].
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Programs
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Maple
with(numtheory); f:=n->pi(2^n+n)-pi(2^n-n-1); [seq(f(n),n=0..20)]; # second Maple program: a:= n-> add(`if`(isprime(t), 1, 0), t=2^n-n..2^n+n): seq(a(n), n=0..100); # Alois P. Heinz, Sep 13 2011
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Mathematica
Table[PrimePi[2^n + n] - PrimePi[2^n - n - 1], {n, 0, 40}]
Extensions
Corrected with Maple program. - N. J. A. Sloane, Jul 11 2011
Corrected name and added terms up to a(40). - T. D. Noe, Jul 12 2011
More terms from Alois P. Heinz, Sep 13 2011